The move also sees Barcelona B midfielder Denis Suarez move to the Ramon Sanchez Pizjuan on a two-season loan deal.
Rakitic's arrival adds to the signing of Marc-Andre ter Stegen, who is replacing Victor Valdes as Barca's first-choice goalkeeper.
The Croatia international's arrival will help fill the void left by Cesc Fabregas' departure to Chelsea.
A stunning season in Seville saw Rakitic score 15 goals and provide 18 assists in 52 appearances as Unai Emery's side won the UEFA Europa League and secured a top-five La Liga finish.
Barca said in a statement: "Ivan Rakitic arrives at Camp Nou after impressing for three seasons with Sevilla.
"He has done nothing but improve in his time at the Sanchez Pizjuan, becoming the team's main central playmaker and captain, leading them to the Europa League title in the 2013-14 season."
Rakitic is currently representing his country at the FIFA World Cup in Brazil and can look forward to making the move to Catalunya in a new era for the Spanish giants as they attempt to put a disappointing 2013/14 campaign behind them.
Gerardo Martino was only able to secure the Supercopa de Espana in a tumultuous season that saw the Argentine step away from his job after failing to overcome Atletico Madrid in a decisive La Liga clash at Camp Nou.
Luis Enrique replaced Martino in the Barca hotseat and the new coach will be hoping Rakitic plays his part in ensuring his first season at the helm is a success.
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